Closed ideals of a quasianalytic Fréchet algebra

Abstract.

In this note, we examine the structure of closed ideals of a quasianalytic weighted Beurling algebra $\cal {A}$. This algebra is contained in ${\cal C}^\infty (\mit\Gamma)$ and contains the set $A^\infty (D)$. Like in a previous article (see [6]), we use division properties and we give a characterization of closed ideals I such that $I\cap A^\infty\! \ne \{ 0\}$. Then, we use a factorization property proved in [2], which allows us to describe all the closed ideals of $\cal {A}$.